Q.

A man is known to speak truth 3 out of 4 times. He takes out a card at random from a well shuffled pack of 52 playing cards, and reports it is  a  king. The probability that its actually a king is

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a

14

b

34

c

45

d

15

answer is D.

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Detailed Solution

E1 : card drawn is a king

 E2 : card drawn is not a king

A : man reports it is a king.

We have\

PE1=452=113,PE2=1213

PAE1=34 and PAE2=14

By the Bayes’ rule

PE1A=PE1PAE1PE1PAE1+PE2PAE2=1133411334+121314=15

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A man is known to speak truth 3 out of 4 times. He takes out a card at random from a well shuffled pack of 52 playing cards, and reports it is  a  king. The probability that its actually a king is